Why is it not possible to overload the ternary operator?

if you could override the ternary operator, you would have to write something like this:

xxx operator ?: ( bool condition, xxx trueVal, xxx falseVal );

To call your override, the compiler would have to calculate the value of both trueVal and falseVal. That's not how the built-in ternary operator works - it only calculates one of those values, which is why you can write things like:

return p == NULL ? 23 : p->value;

without worrying about indirecting through a NULL pointer.

I think the main reason at the time that it didn't seem worth the effort of inventing a new syntax just for that operator. There is no token ?:, so you'd have to create a number of special grammar rules just for it. (The current grammar rule has operator followed by an operator, which is a single token.)

As we've learned (from experience) to use operator overloading more reasonably, it has become apparent that we really shouldn't have allowed overloading of && and || either, for the reasons other responses have pointed out, and probably not operator comma as well (since the overloaded versions won't have the sequence point which the user expects). So the motivation to support it is even less than it was originally.